The present invention generally relates to an apparatus with multiple limbs for positioning and orienting an end component in space and to joints for linking limbs of such an apparatus.
A need exists for simple and effective parallel kinematics mechanisms. Kinematics mechanisms are used in mechanical engineering applications for machining, robotics, positioning devices, coordinate measuring, fixtures and so on. In general, mechanisms can be classified as either serial or parallel. Serial kinematics mechanisms are widely used and presently dominate the market.
A serial kinematics mechanism has a series of cantilever beams that are movably connected together in an end-to-end fashion by prismatic, revolute or spherical joints, forming an open loop. The closer that a member is to a base of the mechanism within the serial structure, the higher the load on that member. Additionally, the farther that a member is from the base, the higher its deflection with respect to the base member. When a serial kinematics mechanism is subjected to loading, the position of the farthest member, i.e., the end-effector, is subject to the cumulative deflections of all serial members. This results in large positioning errors at the end-effector. Being constructed of cantilevers, a serial mechanism has a poor stiffness-to-mass ratio, making such structures bulky in design.
Serial kinematics mechanisms allow fast and easy computation of the position of the end-effector given the position or state of all actuators. In general, this computation is known as the forward kinematics of a mechanism. However, determining the position or state of all actuators given the position of the end-effector, also known as the inverse kinematics, is generally difficult.
Relative to serial kinematics mechanisms, parallel kinematics mechanisms typically have an improved stiffness-to-mass ratio, better accuracy, superior dynamic properties and can move at higher speeds and accelerations. A parallel kinematics mechanism has a plurality of links which form one or more closed loops, the links thereby sharing the load on the end-effector. Links of such a mechanism typically experience only compression or pulling forces allowing the use of cheaper material and simpler link designs. Moreover, positioning errors of actuators are typically divided, thereby resulting in a high accuracy of the end-effector. A well-known parallel kinematics mechanism is the Stewart-Gough Platform which was introduced in 1965 and has since been the subject of extensive study and analysis. A Stewart-Gough Platform mechanism generally includes a movable platform which is connected to a base by six controllable links. For example, U.S. Pat. No. 5,179,525 discloses a general overview on mechanisms that are based on or derived from the Stewart-Gough Platform.
While parallel kinematics mechanisms can provide improved accuracy, stiffness, and high load carrying capacity, they also suffer from significant control drawbacks. Most known parallel kinematics mechanisms have very difficult forward kinematics. The solutions of the forward kinematics are in the form of high-order polynomial equations, which do not allow closed-form solutions to compute the end-effector position. Computationally intensive methods such as numerical approximations must be applied in order to calculate multiple solutions and select the right one. For example, it has been shown that the general form of the Stewart-Gough Platform has forty feasible solutions. For some special forms of the Stewart-Gough Platform, closed-form solutions of the forward kinematics exist. In these special forms, pairs and triples of spherical joints that connect the links to base and platform are concentric. However, the difficulty of manufacturing such joints is well recognized in the art.
Stewart-Gough-type mechanisms typically allow for the positioning and orientation of the movable platform with six degrees of freedom. In general, the position and orientation of the platform are coupled which complicates the controls. Moreover, due to singularities in the workspace and the restricted working range of joints and actuators, the translational and in particular the rotational motion range of the platform is significantly limited. However, many applications, such as machining or assembly operations, require actuation about an axis with multiple or infinite rotations, which is usually accomplished by additional motors or spindles mounted on the end-effector. This means that one of the actuations of these mechanisms is redundant. In addition, many applications, such as flexible assembly operations or 5-axis machining, require a large orientation capability of the end-effector.
Therefore, alternative parallel kinematics mechanisms have been proposed. For example, U.S. Pat. No. 4,776,749 discloses a robotic device with only five actuated positioning members to position and orient a work tool in space. The device uses two concentric ball-and-socket joints, the first of which connects three and the second of which connects the remaining two actuated positioning members at a respective first and second common point. The device thereby forms a bi-tetrahedral arrangement which decouples the positioning and orienting of the work-tool. While this arrangement facilitates structural rigidity and a closed-form solution of the forward kinematics, the concentric joint design significantly restricts the rotational freedom of each positioning member. Moreover, such joints limit the orientation range of the work tool and are difficult to manufacture in a precise and cost-efficient manner.
In order to accomplish a rigid, bi-tetrahedral structure of the mechanism and simple forward kinematics, alternative joints to connect three or more limbs with spherical motion about a common point have been proposed. For example, U.S. Pat. No. 5,657,584 discloses a joint which uses a large number of elements and pins to produce spherical motion of the attached limbs, resulting in a complex and costly structure. Such a joint is not capable of carrying high loads and offers only limited spherical motion to its limbs.
Another parallel kinematics mechanism without a redundant sixth actuator is disclosed in DE 198 40 886 A1. Five actuated elbow-linkages are connected by separate universal joints to a movable platform which can be positioned and oriented in space. The movable platform serves as the central link which connects all elbow-linkages to form closed loops. The arrangement simplifies the joint design, but neither allows for a closed-form solution of the forward kinematics nor for the decoupling of the position and orientation of the movable platform. The arrangement no longer forms a rigid, bi-tetrahedral structure. Additionally, in comparison to the Stewart-Gough Platform the mechanism is reported to only marginally improve the orientation capability of the movable platform.
Yet another parallel kinematics mechanism with five actuated links is presented in DE 101 53 854 C1. Similar to the aforementioned device, a simplified joint design consisting of five pairs of single-axis joints with a common line of rotation is provided to improve manufacturability of the mechanism. However, the arrangement neither allows for a closed-form solution of the forward kinematics problem nor for the decoupling of the end-effector position and orientation. Moreover, structural rigidity is lost by deviating from a purely bi-tetrahedral structure.
It is well recognized in the art that parallel kinematics mechanisms and in particular devices based on the Stewart-Gough Platform or any of the aforementioned disclosures suffer from a small workspace-to-footprint ratio. The end-effector typically has a limited reach which is further reduced when high orientation capability is required at any point in the workspace. The poor workspace-to-footprint ratio is widely considered a critical factor preventing parallel kinematics mechanisms from entering or penetrating the market and successfully competing with serial kinematics mechanisms.
The described disadvantage is not only inherent to all above-mentioned disclosures but also to various parallel kinematics mechanisms which provide less than five or six degrees of freedom at the end-effector. For example, U.S. Pat. No. 4,790,718 discloses a manipulator to position a flange with known orientation in space. By design, the manipulator is mounted on a truss to operate in a top-down fashion, resulting in a large footprint similar in size to the projected workspace volume. Another device for the movement and positioning of an element in space with three or four degrees of freedom is presented by U.S. Pat. No. 4,976,582. Like the previously described manipulator, the device lends itself to being operated under a truss to which it is mounted, resulting in a similar workspace-to-footprint ratio.
To improve the workspace-to-footprint ratio of parallel kinematics mechanisms, alternative designs have been proposed. For example, WO 02/22320 A1 discloses a manipulator to move an object in space with at least three arms. Two arms are mounted on a central column and rotatably actuated to move in horizontal planes while the third arm is actuated to operate in a vertical plane. Links connect the arms to the end-effector which can move around this column in a cylindrical workspace with three translational degrees of freedom. In one of the disclosed manipulators, the actuator of the third arm is mounted on and rotated by one of the other arms, causing additional inertia and asymmetric torque loads for the two arms. Whenever the end-effector is either at a great distance from or in close proximity to the central column, such an arrangement places the third arm in an unfavorable, asymmetric position relative to the other two arms and causes asymmetric stiffness and accuracy characteristics.
WO 02/058895 A1 discloses a similar manipulator which, in addition, includes a linkage connecting the movements of the three arms such that the third arm always remains in the middle between the other two arms. This results in an improved workspace-to-footprint ratio which is comparable to that of serial kinematics mechanisms of the type known as SCARA robots (Selective Compliance Assembly Robot Arm). However, the mechanisms of both disclosures provide no orientation capability and only three translational degrees of freedom at the end-effector. If orientation capability is desired, wrists or other devices must be mounted in series on the end-effector, making the design complex and the mechanism heavy and slow. Moreover, the use of ball-and-socket joints in the links between the end-effector and the arms is preferred in the aforementioned disclosures but is not desirable in many applications. Furthermore, the mechanism requires a large number of degrees of freedom of the passive joints per degree of freedom provided at the end-effector, causing additional costs, backlash, and inaccuracies.
Another manipulator similar to the one shown in WO 02/058895 A1 is disclosed in U.S. Pat. No. 5,539,291. The manipulator employs three drive mechanisms interposed between a base and a moving element to displace and orient the moving element in a cylindrical workspace with three degrees of freedom. Mover elements of two of the drive mechanisms each operate in a transverse plane and determine the radial distance and orientation of the moving element via a connecting rod and an attitude transmission member which keeps the moving element at a constant attitude towards the transverse plane. The third drive mechanism operates in a plane perpendicular to the transverse plane and influences the axial position of the moving element in the cylindrical workspace. Similar to the aforementioned disclosures, the manipulator only provides three translational degrees of freedom and therefore lacks orientation capability of the moving element. Moreover, the preferred implementation of the attitude transmission member as two wheels and cables may be undesirable in terms of manufacturing cost, assembly, accuracy, backlash and manipulator rigidity.
A major concern in many robotics applications is cable management. To connect various utilities such as power, sensors, encoders at joints, or pressure, power or utility lines must be routed along the moving structure of the mechanism, exposing such lines to significant stress and wear. To ensure operational reliability, custom-made power or utility lines are required, causing considerable extra cost.
Another concern particularly with existing serial kinematics mechanisms, such as SCARA or articulated robots, is the lack of scalability and modularity. To vary the output parameters, such as workspace size or shape, stiffness or accuracy characteristics, the entire serial structure including the actuators typically needs to be redesigned and replaced. Thus, offering a wide range of products does not allow for economies of scale.
A need therefore exists to provide a parallel kinematics mechanism that has simple and practical forward kinematics by allowing the solution for the end-effector position in closed-form. A need also exists for a parallel kinematics mechanism with joint structures that allow three or more limbs to be interconnected and facilitate closed-form solutions of the forward kinematics and decoupling of the end-effector position and orientation. Such a joint structure should be compact and cost-efficient in design, enhance the spherical motion range of the interconnected limbs, and should not restrict the workspace and the orientation range of the end-effector of the mechanism.
Furthermore, a need exists for a parallel kinematics mechanism that is accurate and exhibits a large translational and rotational motion range of the end-effector in combination with a high workspace-to-footprint ratio. Such a mechanism should have a rigid, bi-tetrahedral, robust, modular, and scalable design with no redundant actuators and joints and an improved stiffness-to-mass ratio. Moreover, a need exists to provide a fast mechanism with high acceleration capabilities and improved dynamic properties. Ideally, stiffness, accuracy, and acceleration properties of the end-effector should remain similar within the motion range of the end-effector. Furthermore, the mechanism should allow for simple cable management and improved operational reliability with reduced costs.